Wednesday, 19 September 2012

I've recently been involved with a new mathematical project called Everything is Mathematical. A group of Spanish Mathematicians have written a comprehensive set of popular maths books, which have proved so successful that they're being translated into other languages, including English. The team behind the series have joined up with The Times newspaper and Marcus du Sautoy to present the series to the British audience.

But where do I fit it? Well, to generate some interest in the series they're producing a number of maths challenges that can be found on their website (mine is below).

Some of the challenges are
fairly standard and well known, however, there are a couple of gems
in there that I had never seen before! Keep a look out on the
website for the weekly challenges. If you do solve one of the problems there is a
competition you can enter. The winners receive a free subscription to the
entire set of books.

Now since there are 40 in the set and each one is £10, you may need come convincing before you part with your cash. To get you interested I thought I would review one of the books. Of course since I'm working with these guys you'll have to weight my review with the fact that I'm biased :) (although I'll try to remain neutral).

Who are they for?

Based on what I've read I think these books are more suitable for an
older audience. It could certainly appeal to those who were
educated in numerical subjects and then left due to career decisions, but never lost their interest, as
well as those who never really got on with mathematics but realise its
importance. Having said that I could also also see parents buying a set to enhance their children's education as school as well as benefit their own interests.

Appearance

The first thing I noticed about the series is the sheer comprehensiveness of the books. To be honest, I'd be hard pressed to even name 40 different mathematical fields! The books cover all the standard aspects such as geometry, symmetry, probability, etc. but then goes further with books on the mathematics of our senses and perception, artificial intelligence and, of course (my favourite) mathematical biology.

You may think (as I did) that, by spanning so many subjects, each one would be a pamphlet in size. Here, again, I am pleased to say I was surprised. Each book I've seen is a really nice hard back spanning over 100 pages in length. They contain: nice clear diagrams; formulas; anecdotes about the history; fact boxes and even problems to challenge you.

Book number 1.

What about the content?

Well here is my first admission: I haven't actually read the first book. The first one is all about the golden ratio and its geometry and to be honest, I've never been a fan of the golden ratio because even though it has some extremely nice mathematical properties I find that discussions quickly descend into numerology [Rant 1]. So, instead of starting with The Golden Ratio, I jumped straight in with "When Straight Lines Meet" a book all about non-Euclidean geometry.

Now I would've expected the book to have started with easy stuff, y'know setting up the cartesian coordinates and linear geometry leading on to hyperbolic and elliptic geometry later. How wrong could I have been? The first chapter drops you straight in by explaining the taxi cab metric, using the city of el Ensanche as an illustration.

el Ensanche's very regular city set up.

This is certainly one of the strengths of the books. They use of definite, tangible examples allowing them to discuss complex ideas and very quickly outstrip even my knowledge! For example I had never heard of Girolamo Saccheri's contribution to non-Euclidean geometry.

Each chapter is completely different and could potentially be read independently. For getting a deep overview about a specific aspect (history of geometry, curved space in relativity, uses in computing, etc.) then this format is very appealing. However, it lacks an overarching sense of story that will keep you reading all the way through like the best popular science books can.

What is good to see is they're not afraid of displaying mathematical functions and formulas and then challenging you to calculations that actually mean something, e.g. why calculate the length of a line of a sphere when you can calculate the distance between New York and Sydney on the Earth?

Summary

£400 is a steep price for a comprehensive set of popular maths books, although calling them "popular" perhaps does not do them credit. Think of them more as a set of encyclopaedias of the mathematical world, but with each chapter being eminently more readable than a fact driven summary of events.

There is no better set that will give you the range and depth of subjects available. Due to their diverse nature you will discover topics that interest, entertain and even surprise you. Thus, if you have want to see what mathematics can really do outside of the classroom then these books are you.

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[Rant 1] Of course you're going to find things in the golden ratio if you look for it. Any ratio can be found in nature if you look hard enough. I freely admit that in certain cases you can attribute inspiration to the golden ratio, e.g. Le Corbusier's architecture or Dali's and Da Vinci's paintings. However, these are explicit uses. Stating that certain natural phenomena occur in the golden ratio is much dodgier.

To really believe that the ratio is there I would want to understand WHY it is there. This is the essence of mathematical biology. Biologists observe phenomena, mathematicians try to understand its cause. For instance, there are reasons why the golden ratio/ Fibonacci's sequence should appear in sunflower seed packing as it is the optimal packing ratio. Compare this to the claim that your fingers are in the golden ratio and the suggestion that beautiful people are more in the golden ratio than not. Not only are you left asking why but you're suggesting that people who don't fit your rigid proportions are ugly!

An idea not communicated can scarcely be said to exist.

I am a researcher of mathematical biology at the University of Oxford. Although I now do mathematics as a career I remember how hard maths was when I first started. I also remember what caused things to make sense. I try to relay these insights to everyone, with the hope that they, too, will understand.
Home page:
http://people.maths.ox.ac.uk/~woolley/index.htm